Banach空间的加权微分同构群与加权映射群

IF 1.5 3区数学 Q1 MATHEMATICS

Dissertationes Mathematicae Pub Date : 2010-06-29 DOI:10.4064/dm484-0-1

B. Walter

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引用次数: 26

摘要

在这项工作中，我们构造和研究了一类在加权函数空间上建模的无限维李群。特别地，我们构造了Banach空间上的加权微分同态李群。此外，我们还构造了某些类型的加权映射组。在米尔诺意义上证明了加权差分同构群和加权映射群都是正则李群。我们还讨论了前一群的半直积。此外，我们还研究了某些向量场的李代数的可积性。

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Weighted diffeomorphism groups of Banach spaces and weighted mapping groups

In this work, we construct and study certain classes of infinite dimensional Lie groups that are modelled on weighted function spaces. In particular, we construct a Lie group of weighted diffeomorphisms on a Banach space. Further, we also construct certain types of weighted mapping groups. Both the weighted diffeomorphism groups and the weighted mapping groups are shown to be regular Lie groups in Milnor's sense. We also discuss semidirect products of the former groups. Moreover, we study the integrability of Lie algebras of certain vector fields.

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来源期刊

Dissertationes Mathematicae 数学-数学

CiteScore

2.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： DISSERTATIONES MATHEMATICAE publishes long research papers (preferably 50-100 pages) in any area of mathematics. An important feature of papers accepted for publication should be their utility for a broad readership of specialists in the domain. In particular, the papers should be to some reasonable extent self-contained. The paper version is considered as primary. The following criteria are taken into account in the reviewing procedure: correctness, mathematical level, mathematical novelty, utility for a broad readership of specialists in the domain, language and editorial aspects. The Editors have adopted appropriate procedures to avoid ghostwriting and guest authorship.